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Centripetal Force Calculator

Computes the centripetal (centre-seeking) force and acceleration needed to keep a mass moving in a circle of given radius at a given speed, plus the angular velocity, rotation period and rpm.

When to use

You need the force on a car in a bend, a mass on a string, a satellite or a centrifuge sample from mass, tangential speed and radius, or the g-load of circular motion.

Do not use when: You know the angular speed (rpm) rather than the tangential speed (compute v = ω·r first), or the motion is not circular at constant speed.

Formula

centripetal_acceleration = velocity_m_s² / radius_m; centripetal_force_n = mass_kg × velocity_m_s² / radius_m; ω = velocity_m_s / radius_m; period_s = 2π × radius_m / velocity_m_s; rpm = 60 / period_s

Inputs

Parameter	Type	Unit	Required	Description
`mass_kg`	number	kg	yes	Mass of the moving object in kilograms. Range: > 0
`velocity_m_s`	number	m/s	yes	Speed along the circular path in metres per second. Range: > 0
`radius_m`	number	m	yes	Radius of the circular path in metres. Range: > 0

Outputs

Output	Type	Unit	Description
`centripetal_force_n`	number	N	F = m × v² / r, directed toward the centre.
`centripetal_acceleration_m_s2`	number	m/s²	a = v² / r.
`acceleration_g`	number	g	Centripetal acceleration in multiples of 9.80665 m/s².
`angular_velocity_rad_s`	number	rad/s	ω = v / r.
`period_s`	number	s	Time for one revolution, 2π r / v.
`rpm`	number	rpm	60 / period.

Example

1200 kg car at 20 m/s in a 50 m bend: {"mass_kg":1200,"velocity_m_s":20,"radius_m":50} → {"centripetal_force_n":9600,"centripetal_acceleration_m_s2":8,"acceleration_g":0.8158,"angular_velocity_rad_s":0.4,"period_s":15.708,"rpm":3.8197}

0.5 kg on a 0.75 m string at 3 m/s: {"mass_kg":0.5,"velocity_m_s":3,"radius_m":0.75} → {"centripetal_force_n":6,"centripetal_acceleration_m_s2":12,"angular_velocity_rad_s":4,"period_s":1.5708,"rpm":38.1972}

GET https://tttkmbb.com/api/v1/calculate/centripetal-force?mass_kg=1200&velocity_m_s=20&radius_m=50

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/centripetal-force (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/centripetal-force · Markdown: https://tttkmbb.com/physics/centripetal-force.md · JSON definition: https://tttkmbb.com/physics/centripetal-force.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="centripetal-force"
OpenAPI operationId: calculate_centripetal_force
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

HyperPhysics – Centripetal force (reference)
Wikipedia – Centripetal force (reference)
NIST CODATA – standard acceleration of gravity g_n = 9.80665 m/s² (standard)

FAQ

What provides the centripetal force?

Whatever real force points toward the centre: friction for a car in a bend, tension for a string, gravity for a satellite. If that force cannot reach the required value the object leaves the circle.

Is centrifugal force the same thing?

Centrifugal force is the apparent outward force felt in the rotating frame; it has the same magnitude as the centripetal force but is not a real force in an inertial frame.

Related calculators

Force Calculator — Newton's second law in general.
Acceleration Calculator — Linear acceleration from velocity change.
Circle Calculator — Circumference of the circular path.